## Applying Fracture Mechanics to the Design of Low-Alloy Steel Castings

**Patrick Severson**, **Hathibelagal Roshan**,** R. El-Hajjar**, **Pradeep Rohatgi**

Click **here** to see this story as it appears in the January 2018 issue of *Modern Casting*

Many times, castings are rejected because of a flaw that may not have an influence on the performance or life of the part. They are rejected, or repaired, as a conservative way to make sure the part won’t fail when in service. By analyzing fracture mechanics designers can not only optimize the geometry of a casting, they may also be able to determine whether a flaw is truly detrimental, possibly saving thousands of dollars on scrapping or repair.

Many fabrication techniques are used in steel structures for heavy mobile equipment, including forgings, castings, and weldments. Low-alloy steel castings are common among these techniques and can be used as a stand-alone component or incorporated into part of a weldment. When designing steel components for different types of heavy mobile equipment, different failure modes considered include static strength, fatigue (stress life and strain life), buckling, and connection failures (pins, bolts, etc.). However, current methods of analysis do not take advantage of linear elastic or elastic-plastic fracture mechanics to optimize structural design of low-alloy steel cast components.

Current analysis of cast components consists of generalizing the component as an elastic continuum without any defects or inclusions while assuming isotropic stiffness behavior. Multiple static or dynamic load cases that represent a full duty cycle are applied to determine the mean stress, stress range, and von Mises stress throughout the component. Modified Goodman and Miner’s Rule calculations are applied to determine adequate fatigue life while von Mises stresses are compared to yield stresses to determine adequate safety factors.

Fracture toughness is not considered in the analysis of low-alloy steel castings because high safety factors are used to ensure fatigue crack propagation is not an issue. This type of design methodology can lead to over designed components typically resulting in expensive steel structures.

Tensile properties and impact strength are insufficient to characterize the behavior of materials and the corresponding structures they are included in. Modern design approaches require fracture mechanics characterization of materials. Not only would a fracture mechanics approach help optimize structural design, but unnecessary weld repair operations could be avoided if it is determined that stress intensity factors of an existing crack would never get to their critical values.

In turn, this methodology could be applied to other components with different fabrication techniques, leading to optimization of structures throughout an entire machine. Inspection guidelines from ASTM A903 (Magnetic Particle Inspection) and ASTM A609 (Ultrasonic Inspection) can be used to determine minimum fracture toughness values based on an appropriate inspection level when considering fracture mechanics during design.

Applied Fracture Mechanics

The fracture mechanics approach is concerned with predicting the load-carrying capacity of a structure that contains a crack and explores the stress field surrounding the crack-tip. Parameters used for characterizing fracture behavior that are derived in the framework of fracture mechanics are: 1.) pre-exponent and exponent of the Paris curve that is used to describe fatigue crack growth rates; 2.) fracture toughness in the linear elastic and elastic-plastic fracture mechanics regimes based on the stress intensity factor (K) and the energy parameter J-integral; and 3.) tearing modulus (T) defined as the slope of the J-resistance curve for ductile fracture.

Linear elastic fracture mechanics has two approaches: the energy approach and the stress intensity approach. Materials fracture when enough work is done to break the bonds that hold atoms together in the material. Tensile forces must exceed the cohesive force between atoms to break these bonds. The energy approach uses the law of gravity to describe the energy release rate, which is a measurement of the energy available for crack extension. The stress intensity approach is used to describe stresses at the crack-tip in an isotropic linear elastic material.

For specimens with small plastic zones, linear elastic materials can be described using the energy approach or the stress intensity approach. As the plastic zone size increases, it eventually expands past the singularity zone and there is no longer a region of stress.

Linear elastic fracture mechanics is no longer valid once the plastic zone becomes too large when compared to the specimen dimensions. When this becomes the case, elastic-plastic fracture mechanics must be considered.

Elastic-plastic fracture mechanics has two approaches—crack-tip-opening displacement approach and J-integral approach. It was discovered that fracture surfaces move apart during plastic deformation due to blunting. Opening the crack-tip can be used to measure fracture toughness. This approach demonstrates how hot tears can be predicted and how these indicators can be used in a defect analysis with different casting geometries.

Crawler Shoe Case Study

The crawler shoe is a major component in many types of heavy mobile equipment. The crawler shoe is normally a cast component in a variety of different sizes and configurations that largely depend on the overall mass of the machine. Crawler shoe geometry is common in the industry and consists of features such as lugs that connect one shoe to the next, hollow sections near the outside of the shoe, and a solid middle section where much of the machine mass gets transferred to the ground (Figure 1).

For this study, mechanical properties for AISI 8630 were used in the finite element model. Mechanical properties and material composition are shown in Table 1.

The mesh in the basic finite element model consists of Tet10 elements with an average aspect ratio of 1.8553 and standard deviation of 0.5204.

Typical analysis of the crawler shoe consists of applying several static load cases that represent a full duty cycle. For this study, two load cases were applied that represent the mass of the machine on the shoe and crawler track tension from propel. The geometry was optimized to have an overall safety factor of 3 for strength while having acceptable stress life calculated with a Modified Goodman curve. The maximum von Mises stress of the entire duty cycle is 330 MPa and occurs at the fillet between the lug and the rest of the component (Fig. 2).

Stress life calculations are based off a Modified Goodman approach with an endurance limit calculated to be 572 MPa. Figure 3 shows a plot of each nodal stress life calculation. Each node falls below the endurance limit line indicating that crack initiation will not occur during the life of the component.

After a conventional analysis was done using idealized geometry and using a safety factor of 3 for strength, an initial semi-elliptical crack was introduced to determine the stress intensity factor of the crack-tip and the minimum fracture toughness value required for a safety factor of 3 (Fig. 4). Two types of defects can occur in this type of component: surface defect and embedded defect.

Different nondestructive testing techniques are used for inspection of the component based on the nature of the defect. For surface flaws, magnetic particle inspection (ASTM A903) determines acceptable defect sizes. For embedded flaws, ultrasonic inspection can be used (ASTM A609).

For this study, a surface defect was modeled based off Level V acceptance criteria per ASTM A903. Using this approach, the largest acceptable flaw can be modeled based on inspection criteria. The stress intensity factor of this flaw will determine minimum fracture toughness values the material must have.

Conventional analysis determined the location with the highest nominal tensile stresses from the duty cycle. This is the location where a crack was introduced to give the largest stress intensity factor (KI).

Based off Level V acceptance criteria from ASTM A903, an initial semi-elliptical crack with a major and minor radius of 0.37 in. (9.5 mm) and 0.19 in. (4.75 mm) was introduced into the lug portion of the crawler shoe. A safety factor of 3 was used on top of the stress intensity factor to determine minimum fracture toughness values. The safety factor of 3 corresponds to the safety factor used for static strength (Fig. 5-6).

The largest stress intensity factor from the introduction of a semi-ellipical crack based off Level V magnetic particle inspection is 14.8 MPa√m. Using a safety factor of 3, the mininum fracture toughness value must be at least 44.4 MPa√m.

The properties shown in Table 1 and the chemistry listed in Table 2 are experimental results obtained by using 8630 alloy in a quench and tempered condition in the hardness range of 302-315 BHN. The 8630 alloy in this hardness range is used in commercial crawlers today and according to the results, this material has a fracture toughness value of 106 MPa√m at -45°C. This gives an actual safety factor of 7.2, which suggests the component is over designed and there is room for further optimization based on a fracture mechanics approach.

Based on the analysis, a few conclusions can be drawn. First, a material with a minimum KIC value of 44.4 MPa√m must be used to ensure a fracture safety factor of 3. Second, since fracture toughness is being considered in the analysis, the safety factor for strength can be lowered to optimize material and cost. This reduction in material will create higher nominal stresses in the lug area, increasing the stress intensity factor. An optimization exercise can lead to meeting the fracture safety factor criteria of 3 for a Level V inspection while also meeting strength and fatigue criteria. Third, surface flaws larger than the Level V inspection can be tolerated if other requirements are locking the geometry from changes. A KIC value higher than 44.4 MPa√m must be specified if this is the case.

It should be determined how changing the major and minor radii of the crack influences the stress intensity factor. By using closed-form solutions, the stress intensity factor can be plotted as a function of crack depth if the normal tensile stresses in the location are known. The nominal normal tensile stress in that area is 136 MPa (Fig. 7).

Figure 8 shows the non-linear relationship between crack size and stress intensity factor. The relationship also correlates well with the numerical results obtained for the stress intensity factor. Results for the stress intensity factor are 14.8 MPa√m and 14.9 MPa√m for the numerical and analytical solutions, respectively. This is less than a 1% error between the two solutions. Rearranging the equations above shows how allowable stress and crack size changes with different KIC values.

It can be seen in Figure 9 that it becomes impractical to specify fracture toughness values that are too large. For large fracture toughness values, the component would see large scale yielding before the fracture toughness value of a crack is reached. This solution can only be used when the crack is small compared to the component dimensions. Using ASTM A903 and Figure 10, an engineer can specify the fracture toughness value a component should have based off the acceptance level that is referenced from the standard. In this case, KIC should be about 50 MPa√m based off Level V magnetic particle inspection acceptance criteria.

*This article is based on a paper originally presented at the 2017 Metalcasting Congress in Milwaukee (Paper 17-035).*